What's the point of having a mathematical genius in a film if he isn't (a) barking, and (b) adorable underneath? Or, to put it the other way round, what's the point of having a schizophrenic in a film if he's not a mathematical genius - or some kind of genius?

Ron Howard's plodding, pedestrian hagiography of troubled mathematician John Nash - who suffered from paranoid schizophrenia but went on to win the Nobel prize - is taken straight from Dryden's maxim about great wits being sure to madness near allied. It is also a gruesome example of the lie-opic, or lie-ography, in that it coyly excises the gay episodes in the real Nash's life - in particular his arrest for importuning in a public lavatory.

As portrayed by Russell Crowe, Nash may be a hollow-eyed, unshaven, gibbering, briefcase-hugging, equation-chalking nutter, but by golly he's a red-blooded heterosexual nutter, with a beautiful wife played by Jennifer Connelly. There's nothing funny about him, old boy! Enigma, the recent movie about second world war codebreaking at Bletchley Park, did precisely the same thing with the famously gay mathematician Alan Turing. It turned him into a straight fictional hunk, notably cranking up the madness and emotional breakdown - this being, naturally, the family-entertainment translation of "homosexuality".

A Beautiful Mind's view of schizophrenia subscribes unhesitatingly to the Stephen Hawking idea of disability: it is all right as long as it betokens some great mental or spiritual superiority. The movie starts with Nash at the beginning of his career: the awkward, bow-tied young man at Princeton in the late 1940s, a provincial outsider from West Virginia. He is grumpy and charmless, insistent on looking for something profoundly original, while all around him the smoothies and mediocre careerists are publishing and getting on.

Just when he is on the verge of getting thrown out, Nash has a eureka moment. Hanging out with four thrusting young alpha males, he sees five likely chicks cruise into the bar, great-looking gals all of them, but a certain delicious blonde well to the fore. Nash realises that if all five of them make a move on the blonde, she will take fright and none of them will get her, and the other ladies will turn their noses up too, because no one likes being second best. So nobody will get any sex at all. But if they can somehow modify their competitive instincts and come to some understanding about who gets whom, then all of them could be winners in the bedroom stakes.

Nash's resulting paper on game theory - sensationally contradicting 150 years of Adam Smith's self-interest, me-first philosophy - makes his name. It is a nice moment, comparable in its playful simplicity to Marilyn Monroe talking to Einstein about relativity in Terry Johnson's play Insignificance, filmed by Nic Roeg. Ron Howard's movie is keen to stress how Nash's theory has implications for loads of real-world activities, even including the study of "evolutionary biology". The most obvious implication, about the viability of pinko collectivism, is absent, but Nash goes on to prove his patriotism by working for the US government against the Soviets.

It is here that the dark cloud of insanity begins to settle. Invited into the Pentagon to crack Russian codes, Nash is recruited by shadowy Agent Parcher, played by Ed Harris, who tells him about evidence of terrifying conspiracies which only he can decipher. Poor Dr Nash winds up at the laughing academy in a jacket that does up at the back, with electrodes attached to his temples. Parcher was all in his mind, and much else besides - but how much is real?

The movie isn't quite sure. Nash's breakdown is not a metaphor for cold war paranoia because Howard is only interested in an apolitical, "inspirational" story, about triumph over illness. Confusingly, we do know that some of his government work is real, real enough to get him invited to the Pentagon, real enough to get him a real military policeman posted outside his office. So what are the real effects of that?

We can't be certain, other than to be assured that his cold war government work has helped to impress his future wife and established his non-nerd credentials. All we are left with, as Nash is nursed back to quasi-sanity by the love of a good woman - the film smoothes over his real-life rocky marriage - is Nash's loopy obsession with secret codes.

In Darren Aronofsky's 1998 movie Pi, the haunted maths genius Max Cohen believes that he has developed a programme for unlocking the mysteries of existence. It is just as mad as Nash's theory, but Aronofsky treats it with such fierce seriousness and respect that his vision has a riveting kabbalistic power. Nash's codes are just silly - and boring. Even if Ron Howard's approach is preferable because it does not sentimentalise schizophrenia as a form of mysticism, it fails to find the mysticism in pure mathematics either.

Fundamentally, Crowe's performance is a silly, dumbed-down version of his tobacco scientist in Michael Mann's The Insider. There he was a prickly, intelligent human being. His Nash is just a cutely shambling, lovable problem-filled bear of a man. I am looking forward to the day when someone films Beat the Dealer, the autobiography of the statistician Professor Edward O Thorp, who in the 1960s invented card-counting at blackjack, striking terror into every casino owner in Las Vegas. No madness, no pain - just brains, and a lot of cash. That's what I call a genius.